Ok, so by now we've worked our data hardcore in the exercises on the previous pages. We totaled raw numbers, calculated averages, and made pretty plots and histograms to show off the data. Now, we just need to make sure we understand what it says. Let's go back to our fictional survey on social networking, and quickly review our theme question and its data once more.
We asked 50 middle school boys and 50 middle school girls these questions:
- Do you use FaceSpace, MyBook, or both?
- How much time per day do you spend on these sites?
- Are you "friends" with your parents?
- To the best of your knowledge, do your parents monitor your usage?
Here's what we found*:
| Social Networking Data (% that answered yes to question) | Girls | Boys |
|---|---|---|
| MyBook Page | 86% | 66% |
| FaceSpace Page | 30% | 36% |
| Both | 24% | 22% |
| Neither | 8% | 20% |
| "Friend" with Parent | 66% | 50% |
| Parent Monitors | 54% | 30% |
| Mean time spent on these sites | 2.20 hr/day | 1.01 hr/day |
| Time Spent Social Networking | Girls | Boys |
|---|---|---|
| Mean | 2.20 | 1.01 |
| Median | 2.17 | 0.98 |
| Range | 3.75 | 1.88 |
* This is not real data.
Based on all of this data, it is evident that middle school girls in San Francisco do spend more time on social networking websites than boys. Both their mean and medians are significantly higher. In fact, the girls' median is higher than the boys' upper quartile (Q3). In addition, girls are more likely to "friend" their parents and in turn, their parents are more likely to monitor them. Our study has not proven our hypotheses to be true, but it does strongly suggest that they are likely true.
Based on these results, we might want to ask why parents monitor their daughters more than their sons? Why do girls spend so much free time socializing? What are the boys doing with their free time?
Finally, we need to ask if there is anything else we should look at or more questions that we should ask. For example, we could extend our survey beyond San Francisco. We could also try to break the data down by age: do 13-year-olds spend more time on these social networking sites than 12-year-olds?
It's also important to ask why and how we got the numbers we did. Was the data we gathered correct; did students answer truthfully? Could some of the boys have under-reported their time spent on social networking sites? Did some students overestimate their time? These are all great questions to push our statistical experiment further. We bet you can come up with many more!
Example 1
This stem and leaf plot represents the predicted high temperatures for New York City in the next 10 days.
5|7 represents a predicted temperature of 57 degrees Fahrenheit. Using the stem and leaf plot, determine which statement is accurate. a) It is going to be very, very hot during the next 10 days. b) It is going to freeze in the next 10 days. c) The temperature will remain mostly in the 60’s in the next 10 days. d) There is one day during which the temperature is likely to be 30 degrees colder than the other days. |
Example 2
This histogram represents the scores from the last geometry test. They are graphed with a bin width of 7. Which of the following questions about test performance can be answered based on this graph?
a) What were the two most common ranges of scores on the test and why? b) Why did the majority of the class fail the test? c) Why did most of the class get above 90 on the test? d) How did 3 people get 100 on the test? |
Example 3
This box and whisker plot represents the amount of money Mateo earned the past 18 weeks while working at his dad's shop.
What is a reasonable explanation for the outlier and what could it tell us about Mateo’s earnings? a) Mateo earned the same amount of money each day that he worked. b) Mateo’s dad pays him more money just once in every 18 weeks. c) Mateo worked longer than average during one of the 18 weeks so he earned more money. d) Mateo could have worked 20 weeks instead of 18. |
